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If \( \Large 2 log \left(x+1\right)-10g \left(x^{2}-1\right) = log^{2} \), then x equals

A) 1
B) 0
C) 2
D) 3

Correct Answer:




D) 3

Description for Correct answer:

By definition x ≠ 1, =1

Given equation can be written as

\( \Large log \frac{ \left(x+1\right)^{2} }{x^{2}-1} = log2 => \frac{x+1}{x-1}=2 => x = 3\)

Part of solved Logarithms questions and answers : >> Elementary Mathematics >> Logarithms

Comments

Similar Questions

1). The number \( \Large log 2^{7} \) is:

A). an integer

B). a rational number

C). an irrational number

D). a prime number

2). If \( \Large y = 2^{\frac{1}{logx}\left(8\right)} \), then x is equal to:

A). y

B). \( \Large y^{2} \)

C). \( \Large y^{3} \)

D). none of these

3). If \( \Large log_{05} \sin x = 1 - log_{05} \cos x \), then number of solution of \( \Large x ? \left[ -2 \pi , 2 \pi \right] \) is:

A). 1

B). 2

C). 3

D). 4

4). If a, b, c are in GP. then \( \Large log ax^{x}, log_{bx}x, log_{cx}x \) are in:

A). GP

B). HP

C). AP

D). none of these

5). Consider the following statements:
1. Solution of the inequality \( \Large log_{5} \left(x^{2}-11x+43\right)<2 \) is (0, 2)
2. If \( \Large [x - 1]^{ \left(log_{3}x^{2} - 2Logx^{9}\right)} = \left(x - 1\right)^{7} \), then x is 2 and 81.
Which of these is/are correct?

A). only(1)

B). only 2

C). both of these

D). none of these

6). \( \Large log \cos x \sin x \ge 2 \) and \( \Large x \epsilon \left[ 0, 3 \pi \right] \), then \( \Large \sin x \) lines in the interval:

A). \( \Large \left[ 0, \frac{1}{2} \right] \)

B). \( \Large \left[\frac{\sqrt{5}-1}{2}, 1 \right] \)

C). \( \Large \left[ 0, \frac{\sqrt{5}-1}{2} \right] \)

D). none of these

7). If \( \Large log_{2} x + log_{2} y \ge 6 \), then the least value of \( \Large \left(x + y\right) \) is

A). 4

B). 9

C). 16

D). 32

8). If \( \Large 4^{log_{3}\frac{31}{2}} + 9^{log2^{2}} = 10^{log_{x}83} \), (x belongs to R), then x is:

A). 4

B). 9

C). 10

D). none of these

9). Which of the following is not true?

A). \( \Large \frac{1}{log_{3} \pi } + \frac{1}{log_{4} \pi }>2 \)

B). \( \Large log_{3}5 \)

C). \( \Large \sqrt{8x} = \frac{10}{3} => x = 16 \)

D). \( \Large log_{x} \left(a^{2}+1\right)<0 \), (a?0) then 0

10). If \( \Large y = \frac{1}{a^{1-log ax}} \) and \( \Large z = \frac{1}{a^{1+log_{a}y}} \) then x is equal to:

A). \( \Large \frac{1}{a^{1+log_{a}z}} \)

B). \( \Large \frac{1}{a^{z+log_{a}z}} \)

C). \( \Large \frac{1}{a^{1-log_{a}z}} \)

D). none of these